The Art of Fugue (or The Art of the Fugue; German: Die Kunst der Fuge), BWV 1080, is an incomplete work of unspecified instrumentation by Johann Sebastian Bach (1685–1750). Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.
This work consists of 14 fugues and 4 canons in D minor, each using some variation of a single principal subject, and generally ordered to increase in complexity. "The governing idea of the work", as put by Bach specialist Christoph Wolff, "was an exploration in depth of the contrapuntal possibilities inherent in a single musical subject." The word "contrapunctus" is often used for each fugue.
The earliest extant source of the work is an autograph manuscript of the early 1740s, containing 12 fugues and 2 canons. This autograph is typically referred to by its call number of P200 in the Berlin State Library. Three manuscripts for pieces that appear in the revised edition were bundled with P200 at some point before its acquisition by the library.
The revised version was published in May 1751, slightly less than a year after Bach's death. In addition to changes in the order, notation, and material of pieces which appeared in the autograph; it contained 2 new fugues, 2 new canons, and 3 pieces of ostensibly spurious inclusion. A second edition was published in 1752, but differed only in its addition of a preface by Friedrich Wilhelm Marpurg.
In spite of its revisions, the printed edition of 1751 contained a number of glaring editorial errors. The majority of these may be attributed to Bach's relatively sudden death in the midst of publication. Three pieces were included that do not to appear to have been part of Bach's intended order: an unrevised (and thus redundant) version of the second double fugue, Contrapunctus X; a two-keyboard arrangement of the first mirror fugue, Contrapunctus XIII; and a choraleharmonization "Vor deinen Thron tret ich hiermit" ("Herewith I come before Thy Throne"), derived from BWV 668a, and noted in the introduction to the edition as a recompense for the work's incompleteness, having purportedly been dictated by Bach on his deathbed.
The anomalous character of the published order and the Unfinished Fugue have engendered a wide variety of theories which attempt to restore the work to that state originally intended by Bach.
The Art of Fugue is based on a single subject ( play on piano (help·info) or play on organ (help·info)):
which each canon and fugue employs in some variation.
The work divides into seven groups, according to each piece's prevailing contrapuntal device; in both editions, these groups and their respective components are generally ordered to increase in complexity. In the order in which they occur in the printed edition of 1751 (without the aforementioned works of spurious inclusion), the groups, and their components are as follows.
- 1. Contrapunctus I: 4-voice fugue on principal subject, play principal subject (help·info) or play whole contrapunctus (help·info)
- 2. Contrapunctus II: 4-voice fugue on principal subject, accompanied by a 'French' style dotted rhythm motif, play principal subject (help·info)
- 3. Contrapunctus III: 4-voice fugue on principal subject in inversion, employing intense chromaticism, play principal subject (help·info)
- 4. Contrapunctus IV: 4-voice fugue on principal subject in inversion, employing counter-subjects, play principal subject (help·info)
Counter-fugues, in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:
- 5. Contrapunctus V: Has many stretto entries, as do Contrapuncti VI and VII, play principal subject (help·info)
- 6. Contrapunctus VI, a 4 in Stylo Francese: This adds both forms of the theme in diminution, (halving note lengths), with little rising and descending clusters of semiquavers in one voice answered or punctuated by similar groups in demisemiquavers in another, against sustained notes in the accompanying voices. The dotted rhythm, enhanced by these little rising and descending groups, suggests what is called "French style" in Bach's day, hence the name Stylo Francese. play principal subject (help·info)
- 7. Contrapunctus VII, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and diminished versions of the main subject and its inversion.
Double and triple fugues, employing two and three subjects respectively:
- 8. Contrapunctus VIII, a 3: Triple fugue, with three subjects, having independent expositions, play principal subject (help·info)
- 9. Contrapunctus IX, a 4 alla Duodecima: Double fugue, with two subjects occurring dependently, and in invertible counterpoint at the 12th, play principal subject (help·info)
- 10. Contrapunctus X, a 4 alla Decima: Double fugue, with two subjects occurring dependently, and in invertible counterpoint at the 10th, play principal subject (help·info)
- 11. Contrapunctus XI, a 4: Triple fugue, employing the three subjects of Contrapunctus VIII in inversion, play subject (help·info)
Mirror fugues, in which a piece is notated once and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:
- 12. Contrapunctus XII, a 4
- 13. Contrapunctus XIII, a 3
Canons, labelled by interval and technique:
- 14. Canon per Augmentationem in Contrario Motu: Canon in which the following voice is both inverted and augmented.
- 15. Canon alla Ottava: Canon in imitation at the octave
- 16. Canon alla Decima in Contrapunto alla Terza: Canon in imitation at the tenth
- 17. Canon alla Duodecima in Contrapunto alla Quinta: Canon in imitation at the twelfth
The Unfinished Fugue:
- 18. Fuga a 3 Soggetti (Contrapunctus XIV): 4-voice triple fugue (not completed, but likely to have become a quadruple fugue: see below), the third subject of which is based on the BACH motif, B♭ – A – C – B♮ ('H' in German letter notation). play motif (help·info).
Both editions of the Art of Fugue are written in open score, where each voice is written on its own staff. This has led some to conclude that the Art of Fugue was intended as an intellectual exercise, meant to be studied more than heard. The renowned keyboardist and musicologist Gustav Leonhardt, argued that the Art of Fugue was probably intended to be played on a keyboard instrument (and specifically the harpsichord). Leonhardt's arguments included the following:
- It was common practice in the 17th and early 18th centuries to publish keyboard pieces in open score, especially those that are contrapuntally complex. Examples include Frescobaldi's Fiori musicali (1635), Samuel Scheidt's Tabulatura Nova (1624), works by Johann Jakob Froberger (1616–1667), Franz Anton Maichelbeck (de) (1702–1750), and others.
- The range of none of the ensemble or orchestral instruments of the period corresponds to any of the ranges of the voices in The Art of Fugue. Furthermore, none of the melodic shapes that characterize Bach's ensemble writing are found in the work, and there is no basso continuo.
- The fugue types used are reminiscent of the types in The Well-Tempered Clavier, rather than Bach's ensemble fugues; Leonhardt also shows an "optical" resemblance between the fugues of the two collections, and points out other stylistic similarities between them.
- Finally, since the bass voice in The Art of Fugue occasionally rises above the tenor, and the tenor becomes the "real" bass, Leonhardt deduces that the bass part was not meant to be doubled at 16-foot pitch, thus eliminating the pipe organ as the intended instrument, leaving the harpsichord as the most logical choice.
However, opponents of Leonhardt's theory such as Reinhard Goebel argue that:[this quote needs a citation]
- The Art of Fugue is not completely playable on a keyboard. Contrapunctus XII and XIII, for instance, cannot be played on a single keyboard without making awkward jumps or neglecting the main theme, especially on the keyboard instruments of Bach's day, such as the harpsichord or the early pianoforte, both of which lacked a sustain pedal. This is something Bach would never have allowed to happen. (Although Leonhardt notes that there are similarly 'unplayable' passages in The Well-Tempered Clavier.)
- The absence of the basso continuo is only logical since a fugue for string quartet wouldn't have one by default.
There is also the possibility that The Art of Fugue was not intended for one single (type of) instrument, but instead for whatever instruments were at hand. This hypothesis is given weight by the modern recording and concert history of the work: it is variously performed by string quartets, wind quartets, solo keyboardists, electronics, and orchestras.[original research?]
The Unfinished Fugue
A handwritten manuscript of the piece known as the Unfinished Fugue is among the three bundled with the autograph manuscript P200. It breaks off abruptly in the middle of its third section, with an only partially written measure 239. This autograph carries a note in the handwriting of Carl Philipp Emanuel Bach, stating "Über dieser Fuge, wo der Name B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben." ("At the point where the composer introduces the name BACH [for which the English notation would be B♭–A–C–B♮] in the countersubject to this fugue, the composer died.") This account is disputed by modern scholars, as the manuscript is clearly written in Bach's own hand, and thus dates to a time before his deteriorating health and vision would have prevented his ability to write, probably 1748–1749.
Many scholars, including Gustav Nottebohm (1881), Wolff and Davitt Moroney, have argued that the piece was intended to be a quadruple fugue, with the opening theme of Contrapunctus I to be introduced as the fourth subject. The title Fuga a 3 soggetti, in Italian rather than Latin, was not given by the composer but by CPE Bach, and Bach's obituary actually makes mention of "a draft for a fugue that was to contain four themes in four voices". The combination of all four themes would bring the entire work to a fitting climax. Wolff also suspected that Bach might have finished the fugue on a lost page, called "fragment X", on which the composer attempted to work out the counterpoint between the four subjects. The 2016 completion by pianist Kimiko Douglass-Ishizaka rejects the fourth subject theory, opting instead to develop the extant materials in the fugue to completion.
A number of musicians and musicologists have composed conjectural completions of Contrapunctus XIV, notably Boëly, music theoretician Hugo Riemann, musicologists Donald Tovey and Zoltán Göncz, organists Helmut Walcha, David Goode and Lionel Rogg, and Davitt Moroney. Ferruccio Busoni's Fantasia contrappuntistica is based on Contrapunctus XIV, but is more a work by Busoni than by Bach. In 2001 Luciano Berio arranged the contrapunctus for orchestra; while Berio did not complete the fugue in the usual sense, he produced a performing version that allows the composition to fade away gracefully.
In 2007, New Zealand organist and conductor Indra Hughes completed a doctoral thesis about the unfinished ending of Contrapunctus XIV, proposing that the work was left unfinished not because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.
Douglas Hofstadter's book Gödel, Escher, Bach discusses the unfinished fugue and Bach's supposed death during composition as a tongue-in-cheek illustration of Austrian logician Kurt Gödel's first incompleteness theorem. According to Gödel, the very power of a "sufficiently powerful" formal mathematical system can be exploited to "undermine" the system, by leading to statements that assert such things as "I cannot be proven in this system". In Hofstadter's discussion, Bach's great compositional talent is used as a metaphor for a "sufficiently powerful" formal system; however, Bach's insertion of his own name "in code" into the fugue is not, even metaphorically, a case of Gödelian self-reference; and Bach's failure to finish his self-referential fugue serves as a metaphor for the unprovability of the Gödelian assertion, and thus for the incompleteness of the formal system.
Sylvestre and Costa reported a mathematical architecture of The Art of Fugue, based on bar counts, which shows that the whole work was conceived on the basis of the Fibonacci series and the golden ratio. The significance of the mathematical architecture can probably be explained by considering the role of the work as a membership contribution to the Correspondierende Societät der musicalischen Wissenschaften (de), and to the "scientific" meaning that Bach attributed to counterpoint.
- Helmut Walcha (1956, 1970)
- Glenn Gould (1962) incomplete
- Lionel Rogg (1970)
- Marie-Claire Alain (1974, Rotterdam)
- Wolfgang Rübsam (1992)
- Marie-Claire Alain (1993)
- Louis Thiry (1993) on the Silbermann organ of St Thomas' Church, Strasbourg
- Herbert Tachezi (de) (1996) on the Jürgen Ahrend and Gerhard Brunzema (de) organ in St. Johann (Oberneuland) (de), Bremen
- André Isoir (1999) Some movements performed as a duet with Pierre Farago, on the Grenzing organ of Saint-Cyprien in Périgord, France
- Hans Fagius (2000) on the Carsten Lund organ of Garnisons Church Copenhagen, Denmark
- Kevin Bowyer (2001) on the Marcussen organ of Saint Hans Church, Odense, Denmark
- Régis Allard (2007)
- George Ritchie (2010) on the Richards, Fowkes & Co organ of Pinnacle Presbyterian Church in Scottsdale, Arizona. This recording includes as a bonus track an alternative take of the final unfinished fugue with the completion by Helmut Walcha.
- Joan Lippincott (2012)
Notes and references
- Full discography of The Art of Fugue
- Johann Sebastian Bach / L'art de la fugue / The Art of the Fugue – Jordi Savall, Hesperion XX – Alia Vox 9818
- Piano Society: JS Bach – A biography and various free recordings in MP3 format, including Art of Fugue
- Web-essay on The Art of Fugue
- Introduction to The Art of Fugue
- Die Kunst der Fuge (scores and MIDI files) on the Mutopia Project website
- The Art of Fugue: Scores at the International Music Score Library Project (IMSLP)
- The Art of Fugue as MIDI files
- Image of the ending of the final fugue at external site
- Contrapunctus XIV (the reconstructed quadruple fugue) – Carus-Verlag
- Malina, János: The Ultimate Fugue, The Hungarian Quarterly, Winter 2007
- Contrapunctus XIV (reconstruction): Part 1/2, Part 2/2 (YouTube Video)
- Contrapunctus II as interactive hypermedia at the BinAural Collaborative Hypertext
- Synthesized realization and analysis of The Art of Fugue by Jeffrey Hall
- Hughes, Indra (2006). "Accident or Design? New Theories on the unfinished Contrapunctus 14 in JS Bach's The Art of Fugue, BWV 1080", The University of Auckland PhD thesis
- "Johann Sebastian Bach's The Art of Fugue", article Uri Golomb, published in Goldberg Early Music Magazine
- Ars Rediviva: Sound Recordings Library, The Art of Fugue, Contrapunctus VIII
- description of documentary film Desert Fugue
- Electronic realization by Klangspiegel
- Completion of Contrapunctus XIV by Paul Freeman
- Bach, Alphametics and The Art of Fugue
- "Le concert d'Irena Kosikova a fait un tabac", La Dépêche du Midi, 11 August 2014 (in French)
Chamber music and orchestral works by, and transcriptions after, Johann Sebastian Bach
- ^Johann Sebastian Bach, the Learned Musician by Christoph Wolff, p. 433, ISBN 0-393-04825-X.
- ^The autograph manuscript bears the title Die Kunst der Fuga, written in the hand of Bach's son-in-law Johann Christoph Altnickol. This implies that the title was conceived at some point before the printed edition, which is titled Die Kunst der Fuge, but after the completion of the autograph.
- ^The printed indication of "a 2 Clav." and the counterpoint of the added voices do not appear to follow Bach's practice, evidencing that the parts were likely included by the editors of the printed edition to bolster the work.
- ^Helmut Walcha, "Zu meiner Wiedergabe", in Die Kunst Der Fuge BWV 1080, St Laurenskerk Alkmaar 1956 (Archiv Production, Polydor International 1957), Insert pp. 5–11, at p. 7.
- ^"The Art of the Fugue". American Public Media. Retrieved 25 November 2010.
- ^Media, American Public. "The Art of the Fugue". pipedreams.publicradio.org.
- ^ abLeonhardt, Gustav (July 1953). "The Art of Fugue – Bach's Last Harpsichord Work: An Argument". The Musical Times. 39 (3): 463–466. JSTOR 740009.
- ^D. Schulenberg. "Expression and Authenticity in the Harpsichord Music of J.S. Bach". The Journal of Musicology, Vol. 8, No. 4 (Autumn, 1990), pp. 449–476
- ^See e.g. the discussion in Johann Sebastian Bach, the Learned Musician by Christoph Wolff, ISBN 0-393-04825-X.
- ^"Perfectly right for this performer at this time - Kimiko Ishizaka performs The Art of Fugue with her own completion".
- ^University of Auckland News, Volume 37, Issue 9 (May 25, 2007)Archived September 26, 2007, at the Wayback Machine.
- ^The thesis is available online: http://hdl.handle.net/2292/392
- ^Loïc, Sylvestre; Costa, Marco (2011). THE_ART_OF_FUGUE "The Mathematical Architecture of Bach's The Art of Fugue". Il Saggiatore Musicale. 17: 175–196.
- ^ abcThe recordings by Walcha (1970) and Moroney include both their completion of Contrapunctus XIV and the unfinished original, while Bergel's includes only his attempt.
- ^ abPartial performances on organ (Contrapuncti I–IX) and piano (I, II, IV, IX, XI, XIII inversus, and XIV).
- ^The recording, which includes both the unfinished original and Rogg's completion, in the year of its release won the Grand Prix du Disque from the Charles Cros Academy.
- ^Recordings of Musical Offering and Art of Fugue
- ^Published by Accentus Music: CD – J. S. Bach Kunst der Fuge – Zhu Xiao-Mei, Piano, No. ACC 30308
- ^Paolo Borciani and Elisa Pegreffi with Tommaso Poggi and Luca Simoncini, as Quartetto Italiano, CD Nuova Era 7342, recording 1985.See 
- ^Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.
- ^"J.S.Bach: The Art of the Fugue - Die Kunst der Fuge, BWV 1080". www.niederfellabrunn.at.
- ^Jack Stratton: Contrapunctus IX (talkbox) on YouTube
by Jacy Burroughs
1. Carl Philipp Emanuel Bach was the second surviving son of Johann Sebastian and Maria Barbara Bach (Sebastian’s first wife). This year we celebrate the 300th anniversary of his birth. He was born on March 8, 1714.
2. Emanuel never had any music teacher besides his father. There is no evidence that he studied any instrument other than keyboard.
3. Between 1731 and 1738, Emanuel studied law, first at the University of Leipzig and then at the University of Frankfurt an der Oder. At this time, law was a very typical subject of study for university students. Unlike today, the study of law was considered to be more of a general education than a vocational course of study. Sebastian Bach was determined to give all his sons the university education that he lacked to defend them against society’s prejudices that musicians were simple servants.
While enrolled in school at the University of Frankfurt an der Oder, Emanuel supported himself by teaching keyboard lessons, and composing for or directing public concerts and ceremonies. It was during his years at university that Emanuel’s compositional career accelerated.
4. In 1740, he was appointed harpsichordist to Frederick II of Prussia, who was an accomplished flutist, and served as court accompanist for nearly 30 years. Although the accompanist often had to act as soloist, teacher, coach, Kapellmeister, composer and arranger, Emanuel was the least paid musician in the court.
5. Georg Philipp Telemann was Emanuel’s godfather and Kantor and director of music in Hamburg, Germany. Telemann passed away in 1767 and Emanuel left the court of Frederick II to take over Telemann’s post in early 1768.
6. Emanuel was the foremost composer in the empfindsamer Stil or “sensitive style.” It is characterized by abrupt changes of mood with melodies and rhythms patterned after speech. The style was largely associated with solo keyboard works, particularly for the clavichord and early fortepiano. These instruments were more capable of subtle changes in tone and dynamics than the harpsichord.
7. Emanuel wrote Essay on the True Art of Playing Keyboard Instruments, which is one of the most important writings on the subject. C. G. Neefe, Beethoven’s teacher before he moved to Vienna, often used Emanuel’s compositions and his Essay when teaching young Beethoven. Today, it is an important guide to 18th-century keyboard fingering, ornamentation, continuo playing and improvisation.
8. Emanuel was the most prolific of the Bach sons. He composed in every genre, with the exception of opera. His output consists of symphonies, concerti, chamber music, songs, church music and solo keyboard music, the latter being central to his compositional career.
9. While his music is not terribly well known today, Carl Philipp Emanuel Bach played an essential role in the development of classical music. His symphonies, concerti and keyboard sonatas were influential in the evolution of the classical sonata-allegro form. Haydn, Mozart, and Beethoven, who have come to be known as the big three composers in the Classcial period, all cited Emanuel as an influence.
10. To celebrate the 300th birth year of C.P.E. Bach, all six German Bach cities, Hamburg, Potsdam, Berlin, Frankfurt (Oder), Leipzig, and Weimar are hosting a variety of concerts and events.
Click here for Carl Philipp Emanuel Bach sheet music.
Jacy Burroughs is the Online Merchandiser and Social Media Manager at Sheet Music Plus. She is a freelance horn player in the Bay Area.